Tuning Cooperative Behavior in Games with Nonlinear Opinion Dynamics

Shinkyu Park, Anastasia Bizyaeva, Mari Kawakatsu, Alessio Franci, Naomi Ehrich Leonard

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agents' opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others, network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation or coordination.

Original languageEnglish (US)
Pages (from-to)2030-2035
Number of pages6
JournalIEEE Control Systems Letters
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization


  • Game theory
  • decision making
  • distributed control
  • multi-agent systems
  • opinion dynamics


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